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Zerocoin is supposed to solve the problem with Bitcoin anonymity, or pseudonymity. Initially, it was designed as an extension for Bitcoin network. Now the authors plan to create and release the Zerocoin as a new separate crypto-currency with the infrastructure independent from the Bitcoin network. Here is a good explanation of the Bitcoin anonymity problem.

The Bitcoin payment network offers a highly decentralized mechanism for creating and transferring electronic cash around the world. Unfortunately, Bitcoin suffers from a major limitation: since transactions are stored in a public ledger (called the “block chain”) it may be possible to trace the history of any given payment — even years after the fact. Worse, since the Bitcoin ledger is public, any party can recover this information and data mine to identify users and patterns in the transactions. In other words: Bitcoin transactions are conducted in public.The Bitcoin protocol and clients address this in two ways: (1) all Bitcoin transactions are conducted using public keys as identifiers, and these public keys are not linked to individual names. And (2) Bitcoin clients are capable of generating many public keys (“identities”) to help users resist tracking. Unfortunately, a growing body of research indicates that these protections are insufficient. This information may allow data miners to link individual transactions, identify related payments, and otherwise trace the activities of Bitcoin users.